A290314 Fifth diagonal sequence of the Sheffer triangle A094816 (special Charlier).

1, 89, 814, 4179, 15659, 47775, 125853, 296703, 641058, 1290718, 2451449, 4432792, 7686042, 12851762, 20818302, 32792898, 50387031, 75717831, 111527416, 161322161, 229533997, 321705945, 444704195, 606959145, 818737920, 1092450996, 1442995659, 1888139134, 2448944324, 3150241204, 4021147020, 5095638548

Offset

0,2

Comments

See A094816 and A290311.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

O.g.f.: (1 + 80*x + 49*x^2 - 27*x^3 + 2*x^4)/(1-x)^9.

E.g.f: exp(x)*(1 + 88*x + 637*x^2/2! + 2003*x^3/3! + 3472*x^4/4! + 3574*x^5/5! + 2185*x^6/6! + 735*x^7/7! + 105*x^8/8!).

From Colin Barker, Jul 29 2017: (Start)

a(n) = (5760 + 67248*n + 158180*n^2 + 161700*n^3 + 87695*n^4 + 26952*n^5 + 4670*n^6 + 420*n^7 + 15*n^8) / 5760.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

Prog

(PARI) Vec((1 + 80*x + 49*x^2 - 27*x^3 + 2*x^4) / (1 - x)^9 + O(x^50)) \\ Colin Barker, Jul 29 2017

Crossrefs

Cf. A094816, A290311, A290312, A290313.

Sequence in context: A069764 A053580 A239719 * A103548 A241700 A097155

Adjacent sequences: A290311 A290312 A290313 * A290315 A290316 A290317

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 28 2017

Status

approved